surface of enclosed volume

[brad sue]

1. The problem statement, all variables and given/known data
Hi,
I have this problem:
the surfaces r=2 and 4, \theta=30 degrees and 50 degrees, \phi=20 degrees and 60 degrees identify a closed surface.
1- find the enclosed volume.
2- Find the total area of the enclosed surface. ( I think it is a typo from the teacher. It is volume not surface)

The first question is straigth forward
For the secon question I have some issues.



2. Relevant equations
Do I need to take take each element of surface (in spherical coordinates)
dS1=r^2 sin(theta) d\theta d\phi

dS2=r*drd\phi
dS3=\sin\theta*rdrd\phi



3. The attempt at a solution

integrate the according the limits and the total are should be
S= S1+S2+S3
Is my reasonnig correct?
Thank you
B
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution